No, this isn't a scam - yes, this is something that might seem relatively bizzarre and completely fake, but is unfortunately 100% true. I hate to be the bearer of bad news, but in a recent Facebook update (revealed on the official Facebook Developer Blog), all app developers (that's every single developer - not just a few) now have the ability to access your current address and mobile phone number when you add a new third-party application to your account on Facebook.
This situation is actually a bit complicated, so bear with us. From now on, the "Request for Permission" box that all users see when adding new third-party applications will have a new section entitled "Access my contact information," which lists specifically your current address and mobile phone number. Not every game will have this information being requested - the change here is that application developers can now add that stipulation in. That being the case, when you click "Allow," you are actually giving the developer the right to have this information, but it doesn't have to be that way.
Currently, there doesn't seem to be a way to avoid granting this permission to developers, as Facebook has been the one to grant them access in the first place, however, if you remove this personally identifiable information from your account, then all these developers will have access to is a blank line.
If you're worried that you have this sort of information on your account, which is now free for the taking (who knows what kind of sinister things they could do?), meet us behind the break for a guide on how to find it, and remove it.